general relativity - Has the curvature of spacetime been measured at the human scale?

The curvature of spacetime has been observed many times from the deflection of light around massive astronomical objects. But has it been observed around small objects in a lab?

In the Cavendish experiment, the gravitational attraction between two masses does sufficient effect for it to be measured on Earth. Thus, it raises the question whether light deflection from curved spacetime is also measurable in the lab.

If it has not been achieved, how far are we from it? How much precision would be needed?

Answer

Yes. A relatively direct measurement of curvature of spacetime has recently been performed using a 16 cm atom interferometer setup: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.118.183602 (paywalled).

The basic idea of this type of experiment is that a packet of atoms is prepared in a quantum superposition of locations, then recombined much like light on a beamsplitter, and the phase change is read out. The two spatially separated parts of the wavefunction experience difference phase shifts due to the small changes in the local gravitational field. Rather amazingly, the curvature that they measure is not due to the Earth's field- they need something they can move, so that they can show a phase change that depends on its position. So, they measure the curvature from an 84 kg test mass placed near the interferometer. As a result, this is a measurement of curvature on the human scale both in terms of size and in terms of the amount of mass generating the curvature.

Note that the authors make a distinction between this measurement, which equivalently can be seen as a measurement of the (non-local) gravitational tidal force, and the (local) measurement of acceleration at a point or gravitational redshift. This curvature measurement, unlike those two types of measurements, is coordinate-independent and in particular can not be replicated by going into an accelerated frame of reference. To do this, their device actually involves two separate interferometers, whose outputs are themselves interfered to effectively make a comparison between two spatially separated measurements of the gravitational shift.

See here for more details at a relatively accessible level (open access).